Solve the Linear Programming Problem $\mathrm { P } _ { 1 }$

question 193

Multiple Choice

Solve the linear programming problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$ , has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $P _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $P _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

• A) \(11 \mathrm { P } _ { 1 }\) planes and \(7 \mathrm { P } _ { 2 }\) planes
• B) \(7 \mathrm { P } _ { 1 }\) planes and \(11 \mathrm { P } _ { 2 }\) planes
• C) \(5 \mathrm { P } _ { 1 }\) planes and \(17 \mathrm { P } _ { 2 }\) planes
• D) \(9 \mathrm { P } _ { 1 }\) planes and \(13 \mathrm { P } _ { 2 }\) planes

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Definitions:

Call Option

A financial contract that gives the buyer the right, but not the obligation, to buy a stock or other underlying asset at a predetermined price within a specified time period.

Put Option

A financial contract allowing the holder to sell a specific amount of an underlying asset at a predetermined price within a specified time frame.

Hedge Ratio

A ratio used to calculate the amount of derivatives needed to hedge a position or portfolio, often used to minimize risk exposure.

Delta

A measure in financial markets that compares the change in the price of a derivative to the change in the price of its underlying asset.